While researching James' use of the term 'retrograde' I found this set of articles. Fascinating--if you like both a little historical perspective, and are interested in analytical approaches.

http://www.sci.wsu.edu/math/Lessons/Music/

badgas

12-18-2002, 09:33 AM

I looked at that site also, Bongo.
I got lost on the very top line. Matrices. No idea, didn't see a definition.

Anyway, I bookmarked it and will approach it with an open mind as soon as I clear some of the stuff you've already posted from my mind.

Great sites you find.
So much to learn,,,,,

Bongo Boy

12-29-2002, 07:12 AM

It's a big topic, but not a real tough one. A 'matrix' is simply an array of values arranged as a set of rows and columns. If you have n rows and m columns in the 'array' of numbers, it's referred to as "an n by m matrix". The set of rules for manipulating matrices is called 'linear algebra', and usually forms one or two 1-semester courses in high school & college. Many of the rules are very simple and perfectly analogous to the simplest algebra.

Among the simplest uses of the algebra is for solving multiple equations in multiple unknowns ("simultaneous systems of linear equations" :D), such as:

2x + 3y = 10
3x + 4y = 18

The two equations above can be re-written in matrix notation as a single equation, and application of matrix algebra provides a single (x, y) pair that solves both equations. Powerful stuff, especially when you may have 100 equations with 100 unknowns.

The connection that all this has with the article is a bit fuzzy, tho.

the1andonly

12-31-2002, 07:25 PM

very nice indeed. I love composing with 12-tone music. it's a great way to start thinking outside the box.